A Worked Example: Stockpile Volume

A delivery of crushed stone arrives as one conical pile, and the site needs to confirm the pile matches the delivery ticket. This example works that pile from tape measurements to a checked loose volume, then reconciles the result with the ticket.

What does this worked example cover?

One delivered stockpile of 20 mm crushed stone sitting on a level compacted pad. The example covers the starting measurements, the cone calculation, a slope check, an independent cubic-yard cross-check, a ticket reconciliation, and the final quantity record.

All dimensions, ticket figures, and results are stated example fixtures verified by independent calculation. They demonstrate the arithmetic and describe no real pile.

What are the starting measurements?

Measure the base diameter with a tape held across the base through the estimated center. Three readings: 10.1 m, 9.9 m, and 10.0 m. The mean is 10.0 m, so the radius is 5.0 m.

Measure the vertical height with a sighting rod from the documented pad beside the pile. Three readings: 3.0 m, 3.1 m, and 2.9 m. The mean is 3.0 m.

Record the readings before averaging so the source observations stay available. Confirm the shape before choosing the formula: a near-circular base, one central peak, a uniform face slope, and a visible toe all around the pad. The cone model fits this pile. For a pile that does not fit a cone, use the stockpile volume formulas page.

How do you calculate the cone volume?

Use the cone formula for a conical stockpile: volume equals π times radius squared times vertical height, divided by 3.

Cone volume = π × radius² × vertical height ÷ 3

Result: 78.54 m³ loose. Label the state as loose: the material was disturbed in delivery and piling, which is a different state from bank volume in an excavation.

How do you check the slope and the base?

Derive the face slope from the measured dimensions and compare it with the slope the pile actually shows. Face slope = arctan(height ÷ radius) = arctan(3.0 ÷ 5.0) ≈ 31°. The faces of this pile look uniform at about that slope, so the height reading is consistent with the shape.

If the derived slope disagrees with the visible face, recheck the height reading first. A height taken from a soft spot or an estimated peak moves the slope and the volume together.

How does the same pile check in cubic yards?

Convert the metric result: 78.54 m³ × 1.30795062 = 102.73 yd³ loose.

Check the same pile independently from converted inputs. Radius: 5.0 m = 16.4042 ft. Height: 3.0 m = 9.8425 ft.

Volume = π × 16.4042² × 9.8425 ÷ 3 = 2,773.60 ft³ = 102.73 yd³

Two routes give 102.73 yd³ to the displayed precision. When the routes disagree, the input conversions or the arithmetic carry the error, not the pile.

How do you reconcile the pile with the delivery ticket?

The delivery docket states 120 t of 20 mm crushed stone with a stated loose bulk density of 1.50 t/m³. Convert the ticket to the same state as the measurement.

Ticket-implied loose volume = 120 ÷ 1.50 = 80.0 m³

Measured: 78.54 m³ loose. The pile is 1.46 m³, or 1.8%, under the ticket-implied volume.

That 1.8% can hold the tape and rod uncertainty, the toe interpretation, a pad that is not perfectly level, spillage, partial or rejected loads, or a density that does not match the ticket basis. ASTM C29 measures bulk density on a dry basis in loose or compacted condition, and a stockpile’s actual compaction and moisture may differ from the test. Treat the ticket density as stated, not verified.

The project record decides whether a 1.8% difference is acceptable. This example sets no universal tolerance.

What does the quantity record look like?

Keep every quantity in its state with its source. A short record prevents the field measurement, the ticket mass, and the converted volume from becoming one unexplained total.

Where does this number go next?

Send the checked loose volume to the task that matches its state. Turn it into a haulage plan with the stockpile haulage planning guide, compare bank and loose states with the bank vs loose volume guide, or review the common failure points in stockpile volume mistakes. Measure the next pile with the field procedure in how to measure a stockpile.

Safety and professional scope

Volume arithmetic does not select the measurement method for payment quantities, protective systems, equipment, or haul limits. Payment quantities follow the contract measurement provision, and the project specification controls accepted survey practice.

Keep clear of stockpile toes except when loading, and examine piles for instability before approaching them. Take measurements from safe positions through the approved quantity-control method. Quantity planning does not replace drawings, specifications, or a qualified professional.